Summary: In Neil Salkind (Ed.), Encyclopedia of Research Design.
Thousand Oaks, CA: Sage. 2010
Herv´e Abdi Lynne J. Williams
A standard analysis of variance (a.k.a. anova) provides an F-test, which is called an om-
nibus test because it reflects all possible differences between the means of the groups analyzed
by the anova. However, most experimenters want to draw conclusions more precise than
"the experimental manipulation has an effect on participants' behavior." Precise conclusions
can be obtained from contrast analysis because a contrast expresses a specific question about
the pattern of results of an anova. Specifically, a contrast corresponds to a prediction precise
enough to be translated into a set of numbers called contrast coefficients which reflect the
prediction. The correlation between the contrast coefficients and the observed group means
directly evaluates the similarity between the prediction and the results.
When performing a contrast analysis we need to distinguish whether the contrasts are
planned or post hoc. Planned or a priori contrasts are selected before running the experiment.
In general, they reflect the hypotheses the experimenter wanted to test and there are usually
few of them. Post hoc or a posteriori (after the fact) contrasts are decided after the experiment
has been run. The goal of a posteriori contrasts is to ensure that unexpected results are
When performing a planned analysis involving several contrasts, we need to evaluate